2. (Sections , , and ) Second, we propose a simple and intuitive algorithm to solve (REF ).
Our algorithm, MORBiT (Multi-Objective Robust bilevel optimization with Bi- Timescale algorithm), is a single-loop, bi-timescale, stochastic algorithm based on the standard gradient descent-ascent algorithm. We remark that our algorithm is a generalization of the TTSA algorithm [1]} for solving the single-objective bilevel optimization problem. We also show, theoretically, that MORBiT converges to the first-order stationary point of a general weakly convex min-max bilevel optimization problem at a rate of \(\mathcal {O}(\sqrt{n} K^{-2/5})\)  when the outer objective is weakly convex and the inner objectiver is strongly convex. As special cases, we recover the convergence rates of two existing works, TTSA and TR-MAML, but our algorithm is able to capture a much wider set of bilevel optimization problems.
